Linear Degeneracy in a Class of Nonlinear Second-Order Hyperbolic Systems

TL;DR

This paper demonstrates that a class of nonlinear second-order hyperbolic systems has linearly degenerate Lax modes, which may help prevent singularities in related dissipative relativistic fluid models.

Contribution

It establishes linear degeneracy of Lax modes in certain nonlinear hyperbolic systems, providing insights into solution behavior and singularity avoidance.

Findings

Lax modes are linearly degenerate in the studied systems

Supports the idea that solutions avoid singularities in dissipative relativistic fluids

Enhances understanding of wave propagation in nonlinear hyperbolic systems

Abstract

For a class of nonlinear hyperbolic systems of second order the paper shows that all Lax modes associated with their first-order formulations are linearly degenerate. This property holds for recently considered models of dissipative relativistic fluid dynamics, supporting the possibility that solutions to these models generally avoid singularity formation.